Stable cubic metal-semiconductor alloy clusters: X 4 Y 4 (X=Cu,Ag,Au,Ti; Y=C,Si)

Transcription

1 Stable cubic metal-semiconductor alloy clusters: X 4 Y 4 (X=Cu,Ag,Au,Ti; Y=C,Si) S. F. Li, 1 Xinlian Xue, 1 Yu Jia, 1 Gaofeng Zhao, 2 Mingfeng Zhang, 1 and X. G. Gong 3 1 School of Physics and Engineering, Zhengzhou University, Zhengzhou , People s Republic of China 2 Key Laboratory of Material Physics, Institute of Solid State Physics, Chinese Academy of Science, Hefei, People s Republic of China 3 Surface Physics Laboratory and Department of Physics, Fudan University, Shanghai , People s Republic of China Received 20 September 2005; revised manuscript received 6 February 2006; published 4 April 2006; publisher error corrected 5 April 2006 Ab initio calculations have been performed on the electronic structures for some semiconductor-metal alloy clusters Au n Si m n,m=1 4, upon which very stable cubiclike clusters X 4 Y 4 X=Cu,Ag,Au,Ti; Y =C,Si have been found. The calculations show that relativistic effect as well as the ionic bonds may together play the key role in the cubic structures. The large highest occupied lowest unoccupied molecular orbital gaps ev make them attractive for optoelectronic applications and the perfect cubic structures make some of them desirable for cluster-assembled materials, such as one-dimensional nanotubes. DOI: /PhysRevB I. INTRODUCTION As silicon is the most important semiconducting element in microelectronics industry, Si clusters have been extensively investigated both experimentally 1 and theoretically 2,3 for their potential applications as building blocks to build up well-controlled nanostructures. Since the discovery of the very stable cagelike C 60 fullerenes, 4 searching for free standing carbon and carbon-free clusters such as C n and Si n with cagelike structures has attracted much attention during the last decade. Unfortunately, the cagelike structures for pure Si clusters have never been found due to their unfavorable sp 2 hybridization. However, by doping transition metal atoms, hexagonal prism W@Si 12, 5 fullerenelike 16, cubiclike 14 and Frank-Kasper tetrahedral Ti@Si 16 and adodecahedral Zr@Si 20 clusters 6 have been found. All these metal-encapsulated silicon clusters are stabilized by the interaction of the center doped metal atoms with the silicon cages. However, at present, the n assembled nanomaterials are rarely constructed. 7 Gold is a well known typical metal and shows novel properties in atomic scale. Though the d electrons may take part in the bonding and dominate the physical and chemical properties for Au n clusters, the jellium model still successfully predicated that Au n n=2,8,18,20,34 may be magic clusters, which has been confirmed experimentally by mass spectrometry analysis. 8,9 Studies show that due to relativistic effect, 10 which enhanced stronger sd hybridization and dd interaction in gold, up to 13 atoms, small anionic Au n clusters favor planar structures. 11 And recent research predicates that the relativistic effect continues to play a role in the structures and bonding of large Au clusters. The configuration of Au 20 Ref. 12 was found to be a tetrahedral structure with all of the atoms located on the surfaces, which can be considered four triangle Au 10 planes merged together making a quasi-two-dimensional structure. The latest studies show that Au n n=32,33,34,35 clusters can unexpectedly have cagelike structures. 13 The above results proposed a great challenge for the studies of silicon structures. Can we stabilize one class of silicon cage, such as cube, by appealing to gold? PACS number s : Ar, w, f As cubic structures are easily found in human life we expect that cubic structures may exist and even be universal in the microscope world. As the smallest special cage, cubic units may be even more suitable to build up cluster-assembled materials. In this paper, we report that Si 4 and C 4 clusters indeed can be stabilized to almost perfect cubic structure by alloying with four Au atoms. Other stable cubic metalsemiconductor alloy clusters X 4 Y 4 X=Cu,Ag,Au,Ti; Y =C,Si with large highest occupied molecular orbital-lowest unoccupied molecular orbital HOMO-LUMO gaps are also studied. II. CALCULATION DETAILS The calculations are based on the density functional theory DFT with spin-polarized generalized gradient approximation GGA 14 implemented in the VASP code. 15 The interactions of the valence electrons with the ionic cores are described by projected augmented wave PAW 16 method, with a scalar relativistic effect included. The wave functions are expanded in plane waves with an energy cutoff of 400 ev. We use a simple cubic cell of 15 Å edge length with a periodic boundary condition, and the point approximation for Brillouin zone sampling. The ground states of clusters are obtained by comparing the energies of many random configurations followed with optimizations by conjugated gradient CG 17 and simulated annealing methods. In order to explicitly consider the relativistic effect for Au atoms, we have also used the ADF code 18 to do ZORA zero order regular approximation scalar relativistic calculations for solid support. III. RESULTS AND DISCUSSION First of all, we have studied the geometrical and electronic structures for Au n Si m n,m=1 4 clusters. The ground state structures, the binding energies defined with the form of E b = E X n Y m ne X me Y, the HOMO- LUMO gaps E gap and the bond lengths have been presented in Fig. 1. The calculated average Au-Si bond lengths in /2006/73 16 / /$ The American Physical Society

2 LI et al. FIG. 1. The geometrical structures for Au n Si m n,m=1 4 clusters. The HOMO- LUMO gaps E gap and the main bond lengths are marked for all clusters. Two possible growth modes along the solid line and the dotted line are also shown, respectively. Black spheres: Si atoms, gray spheres: Au atoms. crease from 2.25 Å for AuSi dimer to 2.45 Å for Au 4 Si 4 cluster. For every cluster comprising an odd number of gold atoms, we find 1 B magnetic moment. For those clusters with an even number of gold atoms, large HOMO-LUMO gaps ranging from 0.77 to 2.06 ev have been obtained. These results indicate that the electronic structures of silicon clusters may be tunable by doping gold atoms with different stoichiometries. As shown in Fig. 1, Au 4 Si, Au 2 Si 4, and Au 4 Si 4 clusters have 2.06, 1.06 and 2.01 ev HOMO-LUMO gaps, respectively, indicating their high stabilities, which has been confirmed, in the case of Au 4 Si, by experimental work. 19 For the noble metal Au Ag, Cu, electronic configuration s 1 d 10 for the PAW potential has been used in VASP calculation. If we regard that per gold silicon contributes one four valent electron s, Au 4 Si, Au 2 Si 4, and Au 4 Si 4 clusters have 8, 18, and 20 electrons, respectively, which happens to coincide with the magic numbers predicated by the jellium model for gold clusters. However, it seems that Au 2 Si, Au 2 Si 2, and Au 2 Si 3 clusters with large HOMO-LUMO gaps carrying 6, 10, and 14 valence electrons, respectively, failed to be predicated as stable clusters by the jellium model. It is interesting to find that the Au 4 Si 4 cluster prefers cubic structure with about ev binding energy and a 2.01 ev HOMO-LUMO gap, indicating its high inertness. As presented in Fig. 1 and Table I, the bond length of Si-Au is 2.45 Å. The four Au atoms and the four Si atoms are just alternatively located on the eight apexes of one cube with little distortion. From Fig. 1, one can notice that there may be many growth paths from the reactive linear AuSi dimer to the high stable Au 4 Si 4 cluster, however, we assume that the two most possible growth paths may be along the dotted-line path and the solid-line path, respectively. In fact, along the dotted-line path, the four Au atoms will first be grown up one by one and then the four Si atoms have been grown step by step on the Au 4 core. On the contrary, for the solid-line path the four Si atoms will be first grown up. It is also worth mentioning that the geometrical structures for both Si 3 Au 4 and Au 3 Si 4 clusters are just like one cubic removed one apex. If one Si Au atom is added to the removed apex of Si 3 Au 4 Au 3 Si 4 followed with one simple optimization, then TABLE I. Calculated properties of X 4 Y 4 X=Cu,Ag,Au,Ti; Y =C,Si clusters. In the brackets, C and T d represent cubic and tetrahedral configurations, respectively. R Å includes average bond lengths of X-X, X-Y and Y-Y, respectively; E gap ev is a HOMO-LUMO gap; E b ev is the binding energy defined with E b = E X 4 Y 4 4E X 4E Y ; X-C indicates the average charge flow from per X atom to per Y atom in X 4 Y 4 clusters, obtained from Voronoi deformation density VDD 20 analysis. Clusters R Å X-X X-Y Y-Y E b ev E gap ev X-C e Cu 4 C 4 C Ag 4 C 4 C Au 4 C 4 C Cu 4 Si 4 T d Ag 4 Si 4 T d Au 4 Si 4 C Ti 4 C 4 C Ti 4 Si 4 C

3 STABLE CUBIC METAL-SEMICONDUCTOR ALLOY¼ FIG. 2. The geometrical structures for Au 5 Si 4 and Au 4 Si 5 clusters. Black spheres: Si atoms, gray spheres: Au atoms. the cubic Si 4 Au 4 cluster has been obtained. Recent study results declare that both Si 4 and Au 4 show much higher stability relative to their neighbors, 21 which supports our idea that Si 4 and Au 4 cores could be first grown and there may be competition between these two different growth paths. As presented in Fig. 2, the geometrical structure of Au 5 Si 4 Au 4 Si 5 can be obtained by growing one Au Si atom on the edge face of the cubic Au 4 Si 4, with a small distortion of the cube, which again predicates the stability of Au 4 Si 4 cluster. In Fig. 3, we present the dissociation energy for one Au Si atom from Au n Si 4 Au 4 Si m clusters n,m=1 5. Much higher stability for Au 4 Si 4 relative to its neighbors can be seen clearly. We have also further studied the interaction between two cubic Au 4 Si 4 clusters. The reacted product keeps these two cubic units almost intact with about 2.56 Å distance and about 1.66 ev reaction energy E R for two Au 4 Si 4 clusters, E R = E( Au 4 Si 4 2 ) 2E Au 4 Si 4, as shown in the inserted panel in Fig. 3. The HOMO-LUMO gap still reaches about 1.0 ev, which suggests that stable selforganized assemblies of the cubic Au 4 Si 4 unit may be very possible. The relativistic effect may indeed play an important role in the structure for the X 4 Si 4 cluster. As has been mentioned, Au clusters favor planar or cagelike structures due to the relativistic effect, then one may ask a question does the relativistic effect still work in the binary alloy cubic Au 4 Si 4 cluster? In order to make this question clear, we have also studied the electronic structures for Cu 4 Si 4 and Ag 4 Si 4 clusters. The calculated results show that both Cu 4 Si 4 and Ag 4 Si 4 clusters prefer cubiclike structures with relatively large distortion. In fact, the most stable structures for both Cu 4 Si 4 and Ag 4 Si 4 are inlaid tetrahedronlike, which can also be regarded as four metal atoms which adsorb on the four surfaces of the inner Si 4 tetrahedron, constituting the outer tetrahedron. And the ratio of Cu-Cu Ag-Ag distance to that of the Si-Si is FIG. 3. The dissociation energy E d, E d n = E Au Si n Si Au 4 E Au Si E Au Si n 1 Si Au 4 for one Au Si atom from Au n Si 4 Au 4 Si m cluster n,m=1 5. Much higher stability for Au 4 Si 4 relative to its neighbors can be seen clearly. In the inserted figure, the configuration for two reacted Au 4 Si 4 clusters is presented, which also indicates the extraordinary stability of the Au 4 Si 4 cluster. about 1.31 Å 1.55 Å, which can be seen from Table I and Fig. 4. These results indicate that the relativistic effect does work in the cubic Au 4 Si 4 cluster. We have also made the comparison between relativistic and nonrelativistic calculations performed by both VASP and ADF codes for Au 4 Si 4. The calculations performed by both these two codes show that, in a nonrelativistic level, the cubic structure is not stable for Au 4 Si 4, which will distort to the inlaid-tetrahedronlike structure, however, in a relativistic calculation level, the inlaidtetrahedronlike configuration will relax again to cubic structure. Our calculations also show that in the cubic structure owing to the stabilization of s electrons of Au, the charge flow from per Au atom to per Si atom is only about 0.07 e see Table I. While in the inlaid-tetrahedronlike structure obtained with nonrelativistic calculations, the charge flow reaches to about 0.2 e, however, the Au-Si bonding lengths have been lengthened to about 2.68 Å, making the total binding energy decrease. The relativistic effect may be very weak in Cu 4 Si 4 and Ag 4 Si 4 clusters, and these two clusters prefer inlaid-tetrahedronlike structures. These results indicate that the relativistic effect may really play a key role in the cubic structure, though we also guess that the size effect for Cu, Ag, and Au atoms may be important in the structural differences. As the same important semiconducting element silicon, carbon has also attracted much attention for applications in FIG. 4. The geometrical configurations for X 4 Y 4 X=Cu,Ag,Au,Ti; Y =C,Si clusters. The HOMO-LUMO gaps are also marked for each cluster. The black spheres and the gray spheres correspond to the semiconductor atoms and the metal atoms, respectively

4 LI et al. FIG. 5. The average binding energies per atom AE b and the HOMO-LUMO gaps E gap in ev for finite nanotubes of Ti 4 C 4 n n=1,2,3 and for the infinite Ti 4 C 4 nanotube. The structure for the infinite nanotube has also been shown. nanoscience. Can a C 4 cluster also be stabilized to cubic structures by alloying with noble metal atoms? We are surprised to find that the most stable structures for all the X 4 C 4 X=Cu,Ag,Au clusters are almost perfect cubic configurations see Table I and Fig. 4. The bond length of Cu-C in Cu 4 C 4 cluster is 1.91 Å, which is about 10% smaller than the Ag-C and Au-C bond lengths 2.14 Å, 2.15 Å in Ag 4 C 4 and Au 4 C 4 clusters, respectively. There are 2.10, 1.67, and 1.83 ev HOMO-LUMO gaps for X 4 C 4 X=Cu,Ag,Au clusters respectively, indicating their high inertness and stability. As discussed above, due to the relativistic effect, the Au 4 Si 4 cluster can be stabilized to cubic structure. So it is reasonable for Au 4 C 4 to favor cubic configuration. However, it seems difficult to understand the almost perfect cubic structures for X 4 C 4 X=Cu,Ag clusters. In fact, the cubic structures for X 4 C 4 X=Cu,Ag clusters may be understood from the point of view of X-C ionic bonds. As shown in Table I, the charge flow from X X=Cu,Ag,Au to C atom is about e, which is obviously larger than that in X 4 Si 4 X=Cu,Ag clusters with inlaid-tetrahedronlike structures. In the mean time, as all the X 4 C 4 X=Cu,Ag,Au clusters are almost perfect cubic configurations, so we regard that the size effect does not work in a cubic-noncubic alternative in X 4 Si 4 X=Cu,Ag,Au clusters. The results above encourage us to make one conclusion that both the relativistic effect and the ionic bonding may dominate the cubic structures. In order to know whether the semiconductor Y 4 Y =C,Si clusters can be stabilized to cubic structures by alloying with other transitional metal elements, we have also studied the electronic structures of Ti 4 Y 4 Y =C,Si clusters. It is well known that Ti can easily alloy with carbon and silicon. As presented in Fig. 4, the Ti 4 C 4 cluster also prefers perfect cubic structure with about 1.97 Å Ti-C bond length. The 2.24 ev see Table I large HOMO-LUMO gap and the ev large binding energy indicate its extraordinary stability. In fact, intensive work has been done for Ti x C y clusters in both theoretical and experimental fields 22 following the original discovery of the metallocarbohedrenes Met- Cars Ti 8 C 12 by Castleman and co-workers. 23 Wang et al. 22 found that Ti 3 C 8, Ti 4 C 8, Ti 6 C 13, Ti 7 C 13, Ti 9 C 15, and Ti 13 C 22 clusters show abundant magic negative ion peaks in mass spectra, and from Ti 4 C 8 these clusters prefer cubiclike growth pathways. It is interesting that the structure for the Ti 4 C 8 cluster can just be regarded as putting an additional four C atoms on the apexes of the cubic Ti 4 C 4 cluster forming four C-C dimers. The results above strongly imply that the Ti 4 C 4 cluster may be the smallest cubic unit in Ti x C y growths. Ti 4 Si 4 cluster is found to favor cubiclike structure with about 0.8 ratio of Ti-Ti distance to Si-Si distance. Despite the large binding energies, Ti 4 Si 4 has a relatively smaller HOMO-LUMO gap of 0.84 ev, which could be partially attributed to the distortions from perfect cubic structures. The electronic analysis shows that the average charge flow from per Ti atom to per Y Y =C,Si atom is 0.55 e and 0.33 e, respectively, indicating again that the strength of the ionic bonds of Ti-Y Y =C,Si may indeed play an important role in a cubic-noncubic alternative. Here, we simply state that in our calculations Mulliken analysis predicates obviously larger charge flow for Au 4 Si 4,Ti 4 C 4, and Ti 4 Si 4 clusters than VDD does, for example, about one electron charge flow from per Ti atom to per C atom has been obtained with Mulliken analysis for Ti 4 C 4, whereas for other clusters with the Au and Si components, both methods lead to similar results. Recent studies show that both finite and infinite hexagonal silicon nanotubes can be stabilized by the interactions of transition metal atom with hexagonal 12 cluster units, 7 and by using high-resolution transmission electron microscopy, a stable 3 Å in diameter armchair carbon nanotube can be grown inside a multiwalled carbon-carbon nanotube. 24 However, here we simply report that Ti 4 C 4 units can be selforganized to stable finite and infinite quadrate nanotubes with only about 1.99 Å diameter by the strong Ti-C ionic bonding. For the infinite nanotube, k points have been used. As presented in Fig. 5, in the nanotubes, the Ti 4 C 4 units still keep almost perfect cubic symmetry with about 5% bonding lengths increasing along the tube axis. The average binding energy AE b increases from about 5.7 ev for the Ti 4 C 4 cluster to about 7.3 ev for the infinite Ti 4 C 4 nanotube. For the infinite nanotube, the HOMO- LUMO gap has been decreased to about 0.5 ev, indicating its semiconducting character. Constant-temperature 600 K molecular dynamic simulations performed by VASP show that the infinite finite nanotubes still keep almost perfect quadrate symmetry in a time duration of 1 ps with the time step of 1 fs, showing that the Ti 4 C 4 -organized nanotubes are indeed very stable. The details for the cubic nanotubes will be published separately. IV. SUMMARY In summary, we have shown that, due to the relativistic effect and the ionic bonding, semiconducting Y 4 Y =C,Si clusters can be stabilized to cubic structures by alloying with transition metal elements X X=Cu,Ag,Au,Ti. The metalsemiconductor alloy cubic clusters Au 4 Si 4, X 4 C 4 X =Cu,Ag,Au and Ti 4 C 4 clusters have large binding energies and large HOMO-LUMO gaps, making them desirable for self-organized microelectronic devices and other nanoscale device applications. And we also hope such cubic clusters deserve further experimental investigations

5 STABLE CUBIC METAL-SEMICONDUCTOR ALLOY¼ ACKNOWLEDGMENTS The authors are grateful to Zhenyu Zhang for scientific discussions. This work was partially supported by the National Science Foundation of China, the special funds for major state basic research and CAS projects. Some of the calculations were performed at the Center for Computational Science, Hefei Institute of Physical Sciences. 1 J. L. Elkind, J. M. Alford, F. D. Weiss, R. T. Laaksonen, and R. E. Smalley, J. Chem. Phys. 87, ; M. F. Jarrold, Science 252, ; E. C. Honea, A. Ogura, C. A. Murray, K. Raghavachari, W. O. Sprenger, M. F. Jarrold, and W. L. Brown, Nature London 366, K. Raghavachari and V. Logovinsky, Phys. Rev. Lett. 55, ; S. Saito, S. Ohnishi, C. Satoko, and S. Sugano, J. Phys. Soc. Jpn. 55, ; E. Kaxiras, Phys. Rev. Lett. 64, K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. L. Fye, and M. F. Jarrold, Nature London 392, H. W. Kroto, J. R. Heath, S. C. O Brien, R. F. Curl, and R. E. Smalley, Nature London 318, H. Hiura, T. Miyazaki, and T. Kanayama, Phys. Rev. Lett. 86, V. Kumar and Y. Kawazoe, Phys. Rev. Lett. 87, A. K. Singh, T. M. Briere, V. Kumar, and Y. Kawazoe, Phys. Rev. Lett. 91, W. A. de Heer, Rev. Mod. Phys. 65, S. Neukermans, E. Janssens, H. Tanaka, R. E. Silverans, and P. Lievens, Phys. Rev. Lett. 90, P. Pyykkö, Chem. Rev. Washington, D.C. 88, Hannu Häkkinen, Michael Moseler, and Uzi Landman, Phys. Rev. Lett. 89, J. Li, X. Li, H.-J. Zhai, and L.-S. Wang, Science 299, X. Gu, M. Ji, S. H. Wei, and X. G. Gong, Phys. Rev. B 70, ; M. P. Johansson, D. Sundholm, and J. Vaara, Angew. Chem., Int. Ed. 43, J. P. Perdew and Y. Wang, Phys. Rev. B 45, G. Kresse and J. Furthmüller, Phys. Rev. B 54, ; Comput. Mater. Sci. 6, P. E. Blöchl, Phys. Rev. B 50, ; G. Kresse and D. Joubert, ibid. 59, M. P. Teter, M. C. Payne, and D. C. Allan, Phys. Rev. B 40, ADF 2002, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, Netherlands 19 B. Kiran, X. Li, H. J. Zhai, L. F. Cui, and L. S. Wang, Angew. Chem., Int. Ed. 43, ; X. Li, B. Kiran, and L.-S. Wang, J. Phys. Chem. A 109, C. F. Guerra, J.-W. Handgraaf, E. J. Baerends, and F. M. Blckelhaupt, J. Comput. Chem. 25, S. F. Li and X. G. Gong, J. Chem. Phys. 122, ; D. W. Yuan, Y. Wang, and Z. Zeng, ibid. 122, L-S. Wang, S. Li, and H. Wu, J. Phys. Chem. 100, ; X.-B. Wang, C.-F. Ding, and L.-S. Wang, J. Phys. Chem. A 101, ; L.-S. Wang, X. B. Wang, H. Wu, and H. C. Cheng, J. Am. Chem. Soc. 120, ; and the references therein. 23 B.C. Guo, K. P. Kerns, and A. W. Castleman, Jr., Science 255, ; B. C. Guo, S. Wei, J. Purnell, S. Buzza, and A. W. Castleman, Jr., ibid. 256, X. Zhao, Y. Liu, S. Inoue, T. Suzuki, R. O. Jones, and Y. Ando, Phys. Rev. Lett. 92,